What is the period of the function $g(x)=-\sin(-8x-3)+5$ ? Give an exact value. units
Answer: Period in sinusoids of the form $y=a\sin(bx+c)+d$ Graphically, the period of a sinusoidal function is the horizontal distance between the ends of a single cycle of its graph. The period of a sinusoid of the form $y={a}\sin( {b}x + c) + {d}$ is equal to $\dfrac{2\pi}{| b|}$. [How can we justify this given our graphical understanding of period?] Finding the period The period of $g(x) = -\sin({-8}x-3)+5$ is: $\begin{aligned} \text{period}&=\dfrac{2\pi}{|{b}|}\\\\ &=\dfrac{2\pi}{| {-8}|} \\\\\\\\\\ &=\dfrac{2\pi}{8}\\\\\\\\ &= \dfrac{\pi}{4} \\ \end{aligned}$ The answer The period of $g(x) = -\sin({-8}x-3)+5$ is $\dfrac{\pi}{4} $ units.